On the Mittag Leffler Bargmann (MLB) transform
Natanael Alpay, Kamal Diki

TL;DR
This paper introduces a new Segal-Bargmann transform linked to the Mittag Leffler Fock space, explores its connection to the Fourier transform, and extends the framework to quaternionic slice hyperholomorphic functions.
Contribution
It develops the Mittag Leffler Bargmann transform, connects it with Fourier analysis, and extends the theory to quaternionic functions, providing new tools in hyperholomorphic analysis.
Findings
Defined the Mittag Leffler Segal-Bargmann transform
Established its relation to the Fourier transform
Extended results to quaternionic slice hyperholomorphic functions
Abstract
We introduce the Segal-Bargmann transform associated to the Mittag Leffler Fock space and study how it will be connected to the Fourier transform. We will discuss also the counterpart of the creation and annihilation operator in this setting using the Caputo and Liouville operators. Finally, we give an extension of these results to the case of quaternions, in particular in the slice hyperholomorphic setting.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics
